The winter of 1962-63 was the coldest on record in England and Wales in the 20th century. Blizzards began across the north shortly before Christmas and by mid-January temperatures had plummeted to -16C, covering the sea with a solid ice sheet a mile wide at Herne Bay in Kent. Snow lay across much of the country for three months and so many hundreds of football fixtures were postponed that the pools companies, having been forced to void the coupons for three weeks in succession and desperate to preserve their takings, inaugurated the Pools Panel to keep their income flowing.

With clubs dependent on gate receipts as their only stable source of revenue, increasingly desperate measures were employed to thaw out pitches and allow them to restore bank balances diminished by their salary obligations. Blackpool engaged the army to melt the ice on Bloomfield Road with flame-throwers, Chelsea, a rather unlikely venue even then for Boys from the Blackstuff, tried motorway tar burners, others bought sand in 90-ton loads and Halifax Town threw in the towel and opened The Shay as an ice rink.

At Filbert Street, however, the groundsman Bill Taylor had more success. In the summer of 1962 Taylor had relaid the pitch and his decision to treat the topsoil with a blend of fertiliser and weedkiller paid dividends when the chemical reaction generated enough heat to battle the intense frost. Once the snow had been cleared with the help of Foxes fans recruited through the pages of the Leicester Mercury, Taylor covered the grass with straw and sat up all night to feed coke into a dozen burning braziers scattered across the field.

All his diligent work could not defeat a 10-day spell of constant snow in late January yet by the month's end he had Filbert Street ready to host its first home game since Boxing Day, a fourth-round FA Cup tie against Ipswich Town. While some clubs would go as long as 10 weeks without playing, Leicester City were back to work in five.

The story of football in the 1960s is dominated by the victors: Bill Shankly and Sir Matt Busby, Sir Alf Ramsey and Harry Catterick, Joe Mercer and Malcolm Allison, Don Revie and Harry Potts, Bill Nicholson's Double winners and the boys of '66. Leicester City, genuine contenders for the majority of a more competitively egalitarian decade, are seldom mentioned yet, like Tottenham Hotspur, they made three FA Cup final appearances during the '60s. While Spurs won all three, Leicester's ribbons never decorated the trophy.

Underdogs in 1961 and 1969, they went into the 1963 final as firm favourites against a Manchester United side with luminaries as radiant as Bobby Charlton, Denis Law and Pat Crerand. That they did so was the product of their form over the gruelling winter months. As others shivered in inactivity, Leicester City advanced in league and Cup with such style and vigour that the only debate among newspapers was whether to proclaim them "the Ice Kings" or "the Ice Age Champs".

Matt Gillies, the former Bolton captain who had moved into a coaching role four years after joining Leicester in 1952, had been appointed to replace David Halliday as manager in 1958. By 1961, the season they had tried to derail Spurs' push for the Double by defeating them in the league at White Hart Lane before their second attempt to stop them was ruined in the FA Cup final when the full-back Len Chalmers was injured and was forced to hobble about on the wing, Gillies had begun to receive praise for his tactical innovation. The Scot and his resourceful coach Bert Johnson had been impressed by the great Austria and Hungary teams of the 1950s and introduced their version of the "whirl" and the "switch", playing sequences of short probing passes to unlock defences and establishing the concept of positional flexibility, specifically for wing-halves, inside-forwards and wingers.

Two signings in the summer of 1962 helped to refine this blueprint. Mike Stringfellow, a brave, tall energetic left-winger bought from Mansfield, was described by his team-mate, Frank McLintock, as "selfless enough to run all day in the service of the team and selfish enough to bombard the goal at almost every opportunity". He was paired with Davie Gibson, the impish inside-left bought from Hibernian after Gillies was persuaded by Johnson to change his original preference from Motherwell's Pat Quinn. Gibson quickly became City's creator-in-chief, his impeccable control and ability to fizz balls out to Stringfellow as well as swap roles with him, and play sharp, angled passes into the box for the converted centre-forward Ken Keyworth, arrested the slump Leicester had experienced the previous season.

On the other side of the field McLintock, then a dynamic right-half before his late transformation at Arsenal into a commanding centre-back, would often use the space vacated when the inside-right Graham Cross retreated (with the opposition's left-half in pursuit) to bomb forward into his colleague's position. Cross, who also played cricket for Leicestershire, eventually prospered as a centre-half but used those defensive instincts while ostensibly a forward to augment the old back three with an extra body. The beauty of the team was its individuals' ability to play different roles during a game and they used it to catch opponents who were wedded to rigid formations by surprise. Having a world-class goalkeeper in Gordon Banks doubtlessly helped too.

When the blizzards hit the Midlands and south in the week before New Year's Day, City had just consolidated their grip on fourth place with a 5-1 Boxing Day victory over Leyton Orient who were enjoying, or rather enduring, their solitary top-flight season. With January's league fixtures wiped out and only the FA Cup victories at Grimsby and at home over Ipswich surviving, Gillies's training sessions took place indoors at Granby Halls before the manager took the squad to marginally more temperate Brighton. Even there, though, it was freezing. Living through that winter, says McLintock, "was a rotten experience. No matter how much coal we threw on the fire, or how many gallons of steaming hot soup we shovelled down, we went weeks without ever being warm".

On 9 February 1963, thanks to Bill Taylor's exertions, City were at last ready to resume their title challenge after a 45-day hiatus. The lay-off was long enough but when contrasted with Arsenal, who went 63 days between home league fixtures, Everton 70 days and Manchester United 77, it is clear how much Leicester owed to the ground staff. But even after the groundsman's all-night vigils, Banks adopted a strange routine to conquer the conditions. When the braziers had been removed, he said, "the pitch had partly frozen over again, especially the end that lay in the shadow of the club's towering double-decker stand. On my right foot I would have my normal boot with hammer-in leather studs, while on my left I'd wear a boot with moulded rubber studs that offered better footing on hard surfaces. Under my arm I would carry the other two odd boots. Once I knew which end we were to defend in the first half I would change one boot to make a pair."

Keyworth scored twice in a 2-0 victory over Arsenal to resume a run that eventually ended in seven successive league victories. Taking into account the state of the pitch, Leicester adopted a more pragmatic style, pinging long passes from the half-backs out to Stringfellow on the left wing and Howard Riley on the right. Everton, Nottingham Forest and Ipswich were dispatched in February to move City up to second place, though the pack behind them all had games in hand.

On 2 March they visited Anfield and won 2-0 with a performance that invited superlatives. The Observer's Ben Wright, in an unimprovable description of the home side's vivacity under Shankly, wrote: "Liverpool started as they usually do – in an almost hysterical hurry." Leicester, he continued, "took complete command" in "a victory for team work". The Guardian's Eric Todd identified the qualities City possessed: "Flexibility, adaptability, terrifying understanding and common sense are Leicester's greatest assets. Intelligent application of all four have done the rest." Gibson capped a fine display by scoring the second goal, driving Todd to write: "They were craftsmen and cracksmen not burglars and if Gibson was the No1 Raffles, there was not much he could teach his colleagues."

The winning run was finally ended with a 2-2 draw at Blackpool but they recovered to pick up a further six points from the next four games before their unbeaten run in 1963 concluded in defeat at Upton Park. A draw at Old Trafford on Easter Monday was followed by a thrilling 4-3 victory over the same opponents the following night, Keyworth matching Law's hat-trick for Manchester United, putting them top of the table with five games to play.

Regular football had given them an edge in the division but as the ice finally relented, the other leading teams began to catch up. Leicester's players professed themselves happy to have the points in the bag instead of games in hand but injuries to Banks, Keyworth, Gibson and the centre-half Ian King disrupted a settled side and demolished their momentum. Only one point was taken from the remaining five games, giving up nine points, the exact margin the eventual champions Everton, who won four and drew one of theirs, held over City at the end of the season. "Under normal circumstances to finish fourth in the league and have a Cup final to look forward to would be considered a successful season," said Banks. "But to us it felt like relegation."

When they had defeated Liverpool at Hillsborough in the FA Cup semi-final Leicester had been second in the table, three points behind Everton who had played a game more. By the end of the following month, the Leicester Mercury began to talk of victory in the final, not as a crowning glory as it had at the end of April, but as a source of solace.

The semi-final was a remarkable match, so one-sided in Liverpool's favour that Leicester's win was more a case of a mugging than the work of gentlemanly thieves. "Playing them when they were at the top of their game," said McLintock vividly, "was like plastering your face in marmalade then kicking over a wasps' nest." Shankly's team battered City and after Stringfellow's counterattacking 18th-minute goal the wave of Liverpool attacks became relentless. Banks was called on to make more than 30 saves, one of them from Ian St John in injury time, according to McLintock, "the equal of anything he ever did, the Pelé save included". Leicester's victory, he continued, "was the biggest travesty of justice I witnessed during 21 years as a professional".

Something similarly unfair happened after the game. A photograph taken of Banks, King and the left-back, Richie Norman, grinning in amused bewilderment at the act of larceny they had just committed was cropped to leave only the Leicester No1 in the shot and the figure of the Liverpool forward, Ian St John, 10 yards away, trudging off the field in abject misery. When the photograph appeared in a Sunday newspaper, it looked like Banks was taunting St John and it brought reams of hate mail from Liverpool supporters to the England keeper's door. The next time he played at Anfield he was pelted with orange peel, boiled sweets and other, less savoury, missiles.

While Leicester's fourth place was their best in the league since 1928-29 (when they had been runners-up to a team then still called The Wednesday), the season had been dire for Manchester – City were relegated and United finished 19th with only three more points than their neighbours. United were considered a side of brilliant individuals, but one which Matt Busby and Jimmy Murphy were struggling to mould into a team, the exact opposite of Leicester's reputation. The pre-match verdicts were almost unanimous: if Leicester played at their peak, they would win.

Sadly, they were unremittingly awful. Their only moment of hope came on 80 minutes when Keyworth answered goals from Law and David Herd but Herd's second in United's 3-1 victory ended City's brief revival five minutes later. Leicester, wrote Alan Hoby in the Sunday Express, were pulled apart by "a deadly duet danced by those two tartan magicians, Crerand and Law". Crerand's anticipation repeatedly robbed Gibson of the ball and with their playmaker comprehensively snuffed out, wrote Hoby, Leicester resembled "a shabby reflection of good intentions".

The sound of studs is McLintock's memory of his second FA Cup final defeat in three years. "After a win there is the rat-a-tat-tat of jubilant players skipping their way up the concrete tunnel. When you lose there is a slow clack-clack. It sounds like the death march and haunts you for years afterwards."

That evening at the club's post-match banquet at the Dorchester, the Leicester City captain, Colin Appleton, said to his team-mates: "We learned an important lesson today, lads. But for the life of me I don't know what it is." Perhaps the abiding lesson is that Ice Kings, just like ice itself, eventually melt away.